Primitive elements of a connected free bialgebra
Rings and Algebras
2023-09-29 v1
Abstract
We prove that the Lie algebra of primitive elements of a graded and connected bialgebra, free as an associative algebra, over a eld of characteristic zero, is a free Lie algebra. The main tool is a ltration, which allows to embed the associated graded Lie algebra into the Lie algebra of a free and cocommutative bialgebra. The result is then a consequence of Cartier-Quillen-Milnor-Moore's Shirshov-Witt's theorems.
Keywords
Cite
@article{arxiv.2309.16199,
title = {Primitive elements of a connected free bialgebra},
author = {Loïc Foissy},
journal= {arXiv preprint arXiv:2309.16199},
year = {2023}
}